Strong Coupling Problem Research Articles

U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition

In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz gravity without the projectability condition can be eliminated by extending the gauge symmetries of the foliation-preserving diffeomorphisms to include a local U(1) symmetry. As a result, the problems of stability, ghost, strong coupling, and different speeds in the gravitational sector are automatically resolved. In addition, with the detailed balance condition softly breaking, the number of independent coupling constants can be significantly reduced (from more than 70 down to 15), while the theory is still UV complete and possesses a healthy IR limit, whereby the prediction powers of the theory are considerably improved. The strong coupling problem in the matter sector can be cured by introducing an energy scale $M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes the suppression energy of high order derivative terms, and $\Lambda_{\omega}$ the would-be strong coupling energy scale.

Strong coupling problem with time-varying sound speed

For a single scalar field with unit sound speed minimally coupled to Einstein gravity, there are exactly three distinct cosmological solutions which produce a scale invariant spectrum of curvature perturbations in a dynamical attractor background, assuming vacuum initial conditions: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and an adiabatic ekpyrotic phase on a slowly expanding background. Of these three, only inflation remains weakly coupled over a wide range of modes, while the other scenarios can produce at most 12 e-folds of scale invariant and Gaussian modes. In this paper, we investigate how allowing the speed of sound of fluctuations to evolve in time affects this classification. While in the presence of a variable sound speed there are many more scenarios which are scale invariant at the level of the two-point function, they generically suffer from strong coupling problems similar to those in the canonical case. There is, however, an exceptional case with superluminal sound speed, which suppresses non-Gaussianities and somewhat alleviates strong coupling issues. We focus on a particular realization of this limit and show these scenarios are constrained and only able to produce at most 28 e-folds of scale invariant and Gaussian perturbations. A similar bound should hold more generally---the condition results from the combined requirements of matching the observed amplitude of curvature perturbations, demanding that the Hubble parameter remain sub-Planckian and keeping non-Gaussianities under control. We therefore conclude that inflation remains the unique cosmological scenario, assuming a single degree of freedom on an attractor background, capable of producing arbitrarily many scale invariant modes while remaining weakly coupled. Alternative mechanisms must inevitably be unstable or rely on multiple degrees of freedom.

Strong coupling in nonrelativistic general covariant theory of gravity

We study the strong coupling problem in the Horava-Melby-Thompson setup of the Horava-Lifshitz gravity with an arbitrary coupling constant $\lambda$, generalized recently by da Silva, where $\lambda$ describes the deviation of the theory in the infrared from general relativity that has $\lambda_{GR} = 1$. We find that a scalar field in the Minkowski background becomes strong coupling for processes with energy higher than $\Lambda_{\omega} [\equiv (M_{pl}/c_1)^{3/2} M_{pl}|\lambda - 1|^{5/4}]$, where generically $c_1 \ll M_{pl}$. However, this problem can be cured by introducing a new energy scale $M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes the suppression energy of high order derivative terms of the theory.

A new extension of Hořava-Lifshitz gravity and curing pathologies of the scalar graviton

We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.

Stability, ghost, and strong coupling in nonrelativistic general covariant theory of gravity withλ≠1

In this paper, we investigate three important issues: stability, ghost, and strong coupling, in the Horava--Melby-Thompson setup of the Horava-Lifshitz theory with $\ensuremath{\lambda}\ensuremath{\ne}1$, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case $\ensuremath{\lambda}=1$, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton, even with $\ensuremath{\lambda}\ensuremath{\ne}1$. We also study the ghost problem in the FRW background and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes, all with the presence of matter: one is cosmological, and the other is static. We find that the coupling becomes strong for a process with energy higher than ${M}_{\mathrm{pl}}|{c}_{\ensuremath{\psi}}{|}^{5/2}$ in the flat FRW background and ${M}_{\mathrm{pl}}|{c}_{\ensuremath{\psi}}{|}^{3}$ in a static weak gravitational field, where $|{c}_{\ensuremath{\psi}}|\ensuremath{\equiv}|(1\ensuremath{-}\ensuremath{\lambda})/(3\ensuremath{\lambda}\ensuremath{-}1){|}^{1/2}$.

Scale-invariance and the strong coupling problem

The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds — both expanding and contracting — allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in this paper, it is challenging to produce scale-invariant fluctuations that are weakly coupled over the range of wavelengths accessible to cosmological observations. In particular, requiring the background to be a dynamical attractor, the curvature fluctuations are scale-invariant and weakly coupled for at least 10 e-folds only if the background is close to de Sitter space. In this case, the time-translation invariance of the background guarantees time-independent n-point functions. For non-attractor solutions, any predictions depend on assumptions about the evolution of the background even when the perturbations are outside of the horizon. For the simplest such scenario we identify the regions of the parameter space that avoid both classical and quantum mechanical strong coupling problems. Finally, we present extensions of our results to backgrounds in which higher-derivative terms play a significant role.

Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

In this paper, we consider two different issues, stability and strong coupling, raised lately in the newly-proposed Horava-Lifshitz (HL) theory of quantum gravity with projectability condition. We find that all the scalar modes are stable in the de Sitter background, due to two different kinds of effects, one from high-order derivatives of the spacetime curvature, and the other from the exponential expansion of the de Sitter space. Combining these effects properly, one can make the instability found in the Minkowski background never appear even for small-scale modes, provided that the IR limit is sufficiently closed to the relativistic fixed point. At the fixed point, all the modes become stabilized. We also show that the instability of Minkowski spacetime can be cured by introducing mass to the spin-0 graviton. The strong coupling problem is investigated following the effective field theory approach, and found that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism, initially designed for the case without projectability condition, but might be circumvented by the Vainshtein mechanism, due to the non-linear effects. In fact, we construct a class of exact solutions, and show explicitly that it reduces smoothly to the de Sitter spacetime in the relativistic limit.

Hamiltonian analysis of linearized extension of Hořava–Lifshitz gravity

We investigate the Hamiltonian structure of linearized extended Hořava–Lifshitz gravity in a flat cosmological background following the Faddeev–Jackiw's Hamiltonian reduction formalism. The Hamiltonian structure of extended Hořava–Lifshitz gravity is similar to that of the projectable version of original Hořava–Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. In the infrared (IR) limit, however, there is one propagating degree of freedom in the general cosmological background, and that is coupled to the scalar graviton mode. We find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the IR limit. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem.

The Decoupled Control Research of UPQC

The double-loop strong coupling problem was existed in the model of some power devices under dq coordinate system. So the entirely decoupling control of UPQC is impracticability. A novel decoupling method is proposed in the paper [2] and the entirely decoupling model of UPQC is achieved. But the paper [2] is not detailed the design of control system. The UPQC can be controlled by open-loop manner and close-loop manner. Its series part can work as either controlled voltage source mode or controlled current source mode. So is the shunt part. Four detailed control strategies were proposed under two control manners and two control modes. The control results of four control strategies are simulated. It can be proved that every control strategy can realize the control goal and the comparison of them is detailed.

Adaptive Nonlinear Optimal Compensation Control for Electro-hydraulic Load Simulator

Directing to the strong position coupling problem of electro-hydraulic load simulator (EHLS), this article presents an adaptive nonlinear optimal compensation control strategy based on two estimated nonlinear parameters, viz. the flow gain coefficient of servo valve and total factors of flow-pressure coefficient. Taking trace error of torque control system to zero as control object, this article designs the adaptive nonlinear optimal compensation control strategy, which regards torque control output of closed-loop controller converging to zero as the control target, to optimize torque tracking performance. Electro-hydraulic load simulator is a typical case of the torque system which is strongly coupled with a hydraulic positioning system. This article firstly builds and analyzes the mathematical models of hydraulic torque and positioning system, then designs an adaptive nonlinear optimal compensation controller, proves the validity of parameters estimation, and shows the comparison data among three control structures with various typical operating conditions, including proportion-integral-derivative (PID) controller only, the velocity synchronizing controller plus PID controller and the proposed adaptive nonlinear optimal compensation controller plus PID controller. Experimental results show that systems' nonlinear parameters are estimated exactly using the proposed method, and the trace accuracy of the torque system is greatly enhanced by adaptive nonlinear optimal compensation control, and the torque servo system capability against sudden disturbance can be greatly improved.

Lessons from the decoupling limit of Hořava gravity

We consider the so-called "healthy" extension of Horava gravity in the limit where the Stuckelberg field decouples from the graviton. We verify the alleged strong coupling problem in this limit, under the assumption that no large dimensionless parameters are put in by hand. This follows from the fact that the dispersion relation for the Stuckelberg field does not have the desired z = 3 anisotropic scaling in the UV. To get the desired scaling and avoid strong coupling one has to introduce a low scale of Lorentz violation and retain some coupling between the graviton and the Stuckelberg field. We also make use of the foliation preserving symmetry to show how the Stuckelberg field couples to some violation of energy conservation. We source the Stuckelberg field using a point particle with a slowly varying mass and show that two such particles feel a constant attractive force. In this particular example, we see no Vainshtein effect, and violations of the Equivalence Principle. The latter is probably generic to other types of source and could potentially be used to place lower bounds on the scale of Lorentz violation.

TOPOLOGICAL PRINCIPLES IN THE THEORY OF ANDERSON LOCALIZATION

Scaling ideas in the theory of the quantum Hall effect are fundamentally based on topological principles in Anderson localization theory. These concepts have a very general significance and are not limited to replica field theory or disordered systems alone. In this chapter, we will discuss these ideas in several distinctly different physical contexts. We start with a brief overview that spans two and a half decades of experimental research on quantum criticality in strong magnetic fields. Secondly, we address the new understanding of universality that has emerged from the theory of Anderson localization and interaction phenomena. In the last part we show how the experimentally observed quantum phenomena fundamentally alter the way in which strong coupling problems in theoretical physics are perceived.

Cosmological perturbations in Hořava-Lifshitz gravity

We study cosmological perturbations in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz Gravity, a recently proposed potentially ultraviolet-complete quantum theory of gravity. We consider scalar metric fluctuations about a homogeneous and isotropic space-time. Starting from the most general metric, we work out the complete second order action for the perturbations. We then make use of the residual gauge invariance and of the constraint equations to reduce the number of dynamical degrees of freedom. At first glance, it appears that there is an extra scalar metric degree of freedom. However, introducing the Sasaki-Mukhanov variable, the combination of spatial metric fluctuation and matter inhomogeneity for which the action in general relativity has canonical form, we find that this variable has the standard time derivative term in the second order action, and that the extra degree of freedom is nondynamical. The limit $\ensuremath{\lambda}\ensuremath{\rightarrow}1$ is well behaved, unlike what is obtained when expanding about Minkowski space-time. Thus, there is no strong coupling problem for Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity when considering cosmological solutions. We also compute the spectrum of cosmological perturbations. If the potential in the action is taken to be of ``detailed balance'' form, we find a cancellation of the highest derivative terms in the action for the curvature fluctuations. As a consequence, the initial spectrum of perturbations will not be scale-invariant in a general space-time background, in contrast to what happens when considering Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz matter leaving the gravitational sector unperturbed. However, if we break the detailed balance condition, then the initial spectrum of curvature fluctuations is indeed scale-invariant on ultraviolet scales. As an application, we consider fluctuations in an inflationary background and draw connections with the ``trans-Planckian problem'' for cosmological perturbations. In the special case in which the potential term in the action is of detailed balance form and in which $\ensuremath{\lambda}=1$, the equation of motion for cosmological perturbations in the far UV takes the same form as in general relativity. However, in general the equation of motion is characterized by a modified dispersion relation.

Dynamic response of strongly correlated Fermi gases in the quantum virial expansion

By developing a quantum virial expansion theory, we quantitatively calculate the dynamic density response function of a trapped strongly interacting Fermi gas at high temperatures near unitarity. A clear transition from atomic to molecular responses is identified in the spectra when crossing from the BCS to BEC regimes, in qualitative agreement with recent Bragg spectroscopy observations. Our virial expansion method provides a promising way to solve the challenging strong-coupling problems and is applicable to other dynamical properties of strongly correlated Fermi gases.

Comment on “Strong coupling in extended Hořava–Lifshitz gravity” [Phys. Lett. B 685 (2010) 197

We show that, contrary to the claim made in arXiv:0911.1299, the extended Hořava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem. By studying the observational constraints on the model we determine the bounds on the scale of the ultraviolet modification for which the proposal yields a phenomenologically viable, renormalizable and weakly coupled model of quantum gravity.

Strong coupling in Hořava gravity

By studying perturbations about the vacuum, we show that Horava gravity suffers from two different strong coupling problems, extending all the way into the deep infra-red. The first of these is associated with the principle of detailed balance and explains why solutions to General Relativity are typically not recovered in models that preserve this structure. The second of these occurs even without detailed balance and is associated with the breaking of diffeomorphism invariance, required for anisotropic scaling in the UV. Since there is a reduced symmetry group there are additional degrees of freedom, which need not decouple in the infra-red. Indeed, we use the Stuckelberg trick to show that one of these extra modes become strongly coupled as the parameters approach their desired infra-red fixed point. Whilst we can evade the first strong coupling problem by breaking detailed balance, we cannot avoid the second, whatever the form of the potential. Therefore the original Horava model, and its phenomenologically viable extensions do not have a perturbative General Relativity limit at any scale. Experiments which confirm the perturbative gravitational wave prediction of General Relativity, such as the cumulative shift of the periastron time of binary pulsars, will presumably rule out the theory.

Recent progress in heteronuclear long-range NMR of complex carbohydrates: 3D H2BC and clean HMBC

The new NMR experiments 3D H2BC and clean HMBC are explored for challenging applications to a complex carbohydrate at natural abundance of 13C. The 3D H2BC experiment is crucial for sequential assignment as it yields heteronuclear one- and two-bond together with COSY correlations for the 1H spins, all in a single spectrum with good resolution and non-informative diagonal-type peaks suppressed. Clean HMBC is a remedy for the ubiquitous problem of strong coupling induced one-bond correlation artifacts in HMBC spectra of carbohydrates. Both experiments work well for one of the largest carbohydrates whose structure has been determined by NMR, not least due to the enhanced resolution offered by the third dimension in 3D H2BC and the improved spectral quality due to artifact suppression in clean HMBC. Hence these new experiments set the scene to take advantage of the sensitivity boost achieved by the latest generation of cold probes for NMR structure determination of even larger and more complex carbohydrates in solution.

A canonical transformation method for the treatment of a strong coupling problem

The Jahn-Teller effect for strong coupling between a triply degenerate electronic state and a triply degenerate vibrational mode (T × t) has been treated using a unitary transformation method. With this method it was possible to diagonalize the major portion of the interaction and therefore possible to calculate approximate energy levels for moderate to strong coupling. For moderate coupling good agreement was found between our analytical calculation and the numerical calculations (available only for weak to moderate coupling).

Multi‐string theories, massive gravity and the AdS/CFT correspondence

AbstractInfrared modifications of gravity have been proposed over the years as potentially useful phenomenological models. Massive (multi)‐gravity is an interesting class of such theories. The true nature and the ultimate consistency of many of these models remains, however, unclear as one is frequently faced with important problems, e.g. classical instabilities and strong coupling problems which are hard to resolve without a known UV completion of the theory. In this note, we review a recent attempt to study some of these well known problems with the use of the AdS/CFT correspondence. In this context, products of large‐N conformal field theories coupled by multi‐trace interactions in diverse dimensions are used to define quantum multi‐gravity (multi‐string/M theory) on a union of (asymptotically) AdS spaces. One‐loop effects generate a small O(1/N) mass for the gravitons and provide non‐trivial examples of massive multi‐graviton theories.

Fermionic propagators for two-dimensional systems with singular interactions

We analyze the form of the fermionic propagator for two-dimensional fermions interacting with massless overdamped bosons. Examples include a nematic and Ising ferromagnetic quantum-critical points and fermions at a half-filled Landau level. Fermi-liquid behavior in these systems is broken at criticality by a singular self-energy, but the Fermi surface remains well defined. These are strong-coupling problems with no expansion parameter other than the number of fermionic species, $N$. The two known limits, $N⪢1$ and $N=0$, show qualitatively different behavior of the fermionic propagator $G({ϵ}_{k},\ensuremath{\omega})$. In the first limit, $G({ϵ}_{k},\ensuremath{\omega})$ has a pole at some ${ϵ}_{k}$; in the other it is analytic. We analyze the crossover between the two limits. We show that the pole survives for all $N$, but at small $N$ it only exists in a range $O({N}^{2})$ near the mass shell. At larger distances from the mass shell, the system evolves and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular. At $N=0$, the range where the pole exists collapses and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular everywhere.